Answer
Angles at vertex $A: \approx 97.7^\circ, B: \approx 53.5^\circ, C: \approx 28.8^\circ$
Work Step by Step
$ \theta = cos^{-1}\dfrac{AB \cdot AC}{|AB||AC|}=cos^{-1}\dfrac{-2}{15}\approx 97.67 ^ \circ$
$ \theta = cos^{-1}\dfrac{AB \cdot BC}{|AB||BC|}=cos^{-1}\dfrac{11}{3\sqrt {38}}\approx 58.5 ^ \circ$
$ \theta = cos^{-1}\dfrac{AC \cdot BC}{|AC||BC|}=cos^{-1}\dfrac{27}{5\sqrt {38}}\approx 28.8 ^ \circ$
Hence,
Angles at vertex $A: \approx 97.7^\circ, B: \approx 53.5^\circ, C: \approx 28.8^\circ$
